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Title:
Cuspidal curves of higher genus
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Abstract:
The research of algebraic curves in the complex projective plane has a long history, especially the study of rational cuspidal curves (i.e. curves homeomorphic to the sphere and having locally irreducible singularities only). On the other hand, cuspidal curves of higher genus were not studied much in the literature. Our joint work with Daniele Celoria and Marco Golla focused on studying curves of arbitrary genus, but having one single singularity only, the link of which can be described topologically by a torus knot. Using methods form low-dimensional topology (Heegaard Floer correction terms), theory of numerical semigroups, basic number theory (Pell equations) and birational geometry (Orevkov's construction) we were able to give an almost complete classification of possible torus knot types for infinitely many genera. This work is closely related to the work of Maciej Borodzik, Matt Hedden and Charles Livingston.
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